Finite Group Databasebeta

← #13172132

Subgroups — #13172132

Order 1728.

1798 conjugacy classes of subgroups.

The subgroup lattice has 1340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
2C2×C3×#3805C211yesmaximal, characteristic, complemented
3C2×#88814C211yesmaximal, characteristic, complemented
4#11723635C211yesmaximal, characteristic, complemented
5#11723608C211yesmaximal, characteristic, complemented
6C3×#63981C211yesmaximal, characteristic, complemented
7C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
8#11723003C211yesmaximal, characteristic, complemented
9#11722988C211yesmaximal, characteristic, complemented
10#11722974C211yesmaximal, characteristic, complemented
11#11722959C211yesmaximal, characteristic, complemented
12#11722956C211yesmaximal, characteristic, complemented
13#11722949C211yesmaximal, characteristic, complemented
14Dic3×#626C211yesmaximal, characteristic, complemented
15D3×#3722C211yesmaximal, characteristic, complemented
16#10595304—31nomaximal
17#10595254—31nomaximal
18#10594292—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
23C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic, complemented
26C3⋊D3×#67—24no—
27C2×#6292C2211yescharacteristic
28C2×#6291C2211yescharacteristic, complemented
29C2×#6290C2211yescharacteristic
30C2×Dic3×C3⋊D3C2211yescharacteristic
31C2×C3×#627C2211yescharacteristic, complemented
32C2×C3×#626C2211yescharacteristic
33C2×C3×#626C2211yescharacteristic, complemented
34C2×C3×#625C2211yescharacteristic, complemented
35C3×#3805—24no—
36C2×C3×D3×Dic3C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38C2×C3×D3×Dic3C2211yescharacteristic, complemented
39C32×#217C2211yescharacteristic, complemented
40#88814C2211yescharacteristic
41#88814C2211yescharacteristic
42#88814C2211yescharacteristic, complemented
43#88814C2211yescharacteristic, complemented
44#88807C2211yescharacteristic, complemented
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48#88804C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic
53C3×#3722C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×D4×C3⋊D3—31no—
57C2×C3×#237—31no—
58C2×C3×#237—31no—
59C2×D3×#67—31no—
60C2×D3×#67—31no—
61C2×D3×#67—61no—
62C2×#3805D311yescharacteristic, complemented
63#64148—31no—
64#64095—31no—
65C3×#937—31no—
66C3×D4×Dic3—31no—
67C3×#882—31no—
68C3×#67⋊C4—31no—
69#63983—31no—
70#63981—31no—
71#63981D311yescharacteristic, complemented
72#63978—31no—
73#63978—31no—
74#63978—31no—
75#63978—31no—
76#63978—61no—
77#67⋊Dic3D311yescharacteristic, complemented
78Dic3×#67—31no—
79#63970—31no—
80#63966—31no—
81#63966—31no—
82#63966—31no—
83#63966—61no—
84C2×#3722—31no—
85C2×#3722—31no—
86C2×(C2×D3)⋊Dic3—31no—
87C2×(C2×D3)⋊Dic3—31no—
88#63922—31no—
89D3×(C2×D3)⋊C4—31no—
90D3×(C2×D3)⋊C4—31no—
91#63909—31no—
92#63908—31no—
93#63907—31no—
94#63905—31no—
95C4×#626—31no—
96#63893—31no—
97Dic3×D12—31no—
98#63891—31no—
99#63887—31no—
100#63886—31no—
101#63871—31no—
102#63864—31no—
103#63852—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—22no—
108C22×C3×C3⋊D3—41no—
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C22×C32×D3C2311yescharacteristic
112C22×C32×D3C2311yescharacteristic
113C2×D3×C3⋊D3—22no—
114C2×D3×C3⋊D3—22no—
115C2×D3×C3⋊D3—41no—
116#6312—22no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3×C3⋊Dic3—22no—
119C2×C3×C3⋊Dic3—41no—
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C32×#67—22no—
125C32×#67D414yescomplemented
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130#6292—22no—
131#6291—41no—
132#6290—22no—
133Dic3×C3⋊D3—22no—
134C3×#627—22no—
135C3×#626—22no—
136C3×#626—41no—
137C3×#625—22no—
138C3×D3×Dic3—22no—
139C3×D3×Dic3—22no—
140C3×D3×Dic3—41no—
141#5829—91no—
142#5591—91no—
143#5554—91no—
144C23×C3⋊D3—31no—
145C23×C3⋊D3C2×D311yescharacteristic
146C23×C3×D3—31no—
147C23×C3×D3—31no—
148C23×C3×D3—61no—
149C22×D32—31no—
150C22×D32—31no—
151C22×D32—61no—
152C2×C32×D4—31no—
153C2×C32×D4—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—31no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638—61no—
160C2×#638—61no—
161C2×#638—61no—
162C2×#638—121no—
163C22×C3⋊Dic3C2×D311yescharacteristic, complemented
164C22×C3⋊Dic3C2×D311yescharacteristic, complemented
165D4×C3⋊D3—64no—
166C2×C4⋊(C3⋊D3)—31no—
167C2×C4×C3⋊D3—31no—
168C2×C3×#67—21no—
169C2×C3×#67—21no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67C2×D311yescharacteristic
175C2×C3×#67C2×D311yescharacteristic
176C2×C3×#67C2×D311yescharacteristic, complemented
177C2×C3×#67C2×D311yescharacteristic, complemented
178C22×C3×Dic3—31no—
179C22×C3×Dic3—31no—
180C22×C3×Dic3—31no—
181C22×C3×Dic3—31no—
182C22×C3×Dic3—31no—
183C22×C3×Dic3—31no—
184C22×C3×Dic3—31no—
185C22×C3×Dic3—61no—
186C22×C3×Dic3—61no—
187C3×#237—64no—
188C3×#237—64no—
189C2×C3×D12—31no—
190C2×C3×D12—31no—
191C2×C3×C4×D3—31no—
192C2×C3×C4×D3—31no—
193C2×C3×C4×D3—31no—
194C2×C3×Dic6—31no—
195C2×C3×Dic6—31no—
196D3×#67—68no—
197D3×#67—64no—
198D3×#67—64no—
199C2×#627C2×D311yescharacteristic, complemented
200C2×#626—31no—
201C2×#626—31no—
202C2×#626—31no—
203C2×#626—31no—
204C2×#626—61no—
205C2×#626—61no—
206C2×#626C2×D311yescharacteristic
207C2×#626C2×D311yescharacteristic, complemented
208C2×#625—31no—
209C2×#625—31no—
210C2×#625—61no—
211C2×#625C2×D311yescharacteristic, complemented
212#3805—24no—
213C2×D3×Dic3—31no—
214C2×D3×Dic3—31no—
215C2×D3×Dic3—61no—
216C2×D3×Dic3C2×D311yescharacteristic, complemented
217C2×D3×Dic3C2×D311yescharacteristic, complemented
218C2×D3×Dic3C2×D311yescharacteristic, complemented
219C32×C22⋊C4—31no—
220#3757—31no—
221#3752—31no—
222#3752—31no—
223#3752—31no—
224C4⋊(C3⋊Dic3)—31no—
225C4⋊(C3⋊Dic3)—31no—
226#3750—31no—
227C3×#217—21no—
228C3×#217—31no—
229C3×#217C2×D311yescharacteristic, complemented
230C3×#217C2×D311yescharacteristic, complemented
231C3×(C2×D3)⋊C4—31no—
232C3×(C2×D3)⋊C4—31no—
233C3×(C2×D3)⋊C4—31no—
234C3×(C2×D3)⋊C4—31no—
235C3×(C2×D3)⋊C4—31no—
236C3×C4⋊Dic3—31no—
237C3×Dic3⋊C4—31no—
238C3×C4×Dic3—31no—
239C3×C4×Dic3—31no—
240Dic3⋊Dic3—31no—
241Dic3⋊Dic3—31no—
242Dic3⋊Dic3—31no—
243Dic3⋊Dic3—31no—
244Dic3⋊Dic3—31no—
245Dic3⋊Dic3—31no—
246Dic3⋊Dic3—61no—
247Dic3⋊Dic3—61no—
248Dic3⋊Dic3—61no—
249Dic3⋊Dic3C2×D311yescharacteristic, complemented
250#3722—31no—
251#3722—31no—
252#3722—31no—
253#3722—31no—
254#3722—31no—
255#3722—31no—
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—61no—
261#3722—61no—
262#3722—61no—
263#3722C2×D311yescharacteristic
264#3722C2×D311yescharacteristic, complemented
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—31no—
272(C2×D3)⋊Dic3—31no—
273(C2×D3)⋊Dic3—31no—
274(C2×D3)⋊Dic3—31no—
275(C2×D3)⋊Dic3—61no—
276(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
277Dic32C2×D311yescharacteristic, complemented
278C22×C33—21no—
279C22×C33—21no—
280C22×C33C2×D412yes—
281C22×C33C2411yescharacteristic
282C2×C3⋊(C3⋊D3)—21no—
283C2×C3⋊(C3⋊D3)—21no—
284C2×C3⋊(C3⋊D3)—21no—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—44no—
291C2×C3×C3⋊D3#4112yescomplemented
292C2×C32×D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3—21no—
296C2×C32×D3—21no—
297C2×C32×D3C2×D412yes—
298D3×C3⋊D3—44no—
299C3⋊(C3⋊Dic3)—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3—21no—
307C32×Dic3C2×D412yes—
308C2×C3×#41—91no—
309C22×#67—91no—
310C2×#237—31no—
311C2×#237—31no—
312C2×D3×D4—91no—
313C2×D3×D4—91no—
314C2×D3×D4—181no—
315C3×#120—91no—
316C3×C4×D4—91no—
317C2×#217—91no—
318#947—91no—
319#946—91no—
320#939—91no—
321#939—91no—
322#939—91no—
323#939—91no—
324#939—181no—
325#938—91no—
326#937—31no—
327#937—91no—
328#937—91no—
329D4×Dic3—31no—
330D4×Dic3—91no—
331#930—91no—
332#930—91no—
333#930—91no—
334#929—91no—
335#929—91no—
336C4×#67—91no—
337C2×(C2×D3)⋊C4—91no—
338C2×(C2×D3)⋊C4—91no—
339C2×(C2×D3)⋊C4—91no—
340C2×(C2×D3)⋊C4—91no—
341#897—91no—
342#895—91no—
343#886—91no—
344#886—91no—
345#886—91no—
346#886—181no—
347#885—91no—
348#883—91no—
349#882—31no—
350#882—91no—
351#67⋊C4—31no—
352D3×C22⋊C4—91no—
353#878—91no—
354#875—91no—
355C4×D12—91no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—21no—
359C23×C32—31no—
360C23×C32—31no—
361C23×C32—41no—
362C23×C32C22×D311yescharacteristic
363C23×C32C22×D311yescharacteristic
364C23×C32C22×D311yescharacteristic
365C22×C3⋊D3—22no—
366C22×C3⋊D3—22no—
367C22×C3⋊D3—31no—
368C22×C3⋊D3—31no—
369C22×C3⋊D3—31no—
370C22×C3⋊D3—41no—
371C22×C3⋊D3—61no—
372C22×C3⋊D3—61no—
373C22×C3⋊D3—61no—
374C22×C3⋊D3—62no—
375C22×C3⋊D3—62no—
376C22×C3⋊D3—121no—
377C22×C3⋊D3—121no—
378C22×C3⋊D3C22×D311yescharacteristic
379C22×C3⋊D3C22×D311yescharacteristic
380C22×C3×D3—21no—
381C22×C3×D3—21no—
382C22×C3×D3—31no—
383C22×C3×D3—31no—
384C22×C3×D3—31no—
385C22×C3×D3—31no—
386C22×C3×D3—61no—
387C22×C3×D3—61no—
388C22×C3×D3—62no—
389C22×C3×D3—62no—
390C22×C3×D3—64no—
391C22×C3×D3—62no—
392C22×C3×D3—62no—
393C22×C3×D3—122no—
394C22×C3×D3—121no—
395C22×C3×D3—121no—
396C22×C3×D3—122no—
397C22×C3×D3C22×D311yescharacteristic
398C22×C3×D3C22×D311yescharacteristic
399C22×C3×D3C22×D311yescharacteristic
400C22×C3×D3C22×D311yescharacteristic
401C2×D32—62no—
402C2×D32—62no—
403C2×D32—64no—
404C2×D32—62no—
405C2×D32—62no—
406C2×D32—122no—
407C2×D32—121no—
408C2×D32—121no—
409C2×D32—122no—
410C32×D4—34no—
411C32×D4—62no—
412C2×C32×C4—31no—
413C2×C32×C4—31no—
414C2×C32×C4—31no—
415C2×C32×C4—31no—
416#638—62no—
417#638—62no—
418#638—64no—
419#638—62no—
420#638—62no—
421#638—122no—
422#638—122no—
423#638—124no—
424#638—121no—
425C2×C3⋊Dic3—22no—
426C2×C3⋊Dic3—31no—
427C2×C3⋊Dic3—31no—
428C2×C3⋊Dic3—31no—
429C2×C3⋊Dic3—41no—
430C2×C3⋊Dic3—61no—
431C2×C3⋊Dic3—61no—
432C2×C3⋊Dic3—61no—
433C2×C3⋊Dic3—121no—
434C2×C3⋊Dic3C22×D311yescharacteristic
435C2×C3⋊Dic3C22×D311yescharacteristic
436C2×C3⋊Dic3C22×D311yescharacteristic
437C2×C3⋊Dic3C22×D311yescharacteristic
438C4⋊(C3⋊D3)—62no—
439C4×C3⋊D3—62no—
440C3×#67—22no—
441C3×#67—22no—
442C3×#67—24no—
443C3×#67—42no—
444C3×#67—62no—
445C3×#67—62no—
446C3×#67—62no—
447C3×#67—121no—
448C3×#67D1214yescomplemented
449C3×#67#6714yescomplemented
450C2×C3×Dic3—21no—
451C2×C3×Dic3—21no—
452C2×C3×Dic3—21no—
453C2×C3×Dic3—21no—
454C2×C3×Dic3—31no—
455C2×C3×Dic3—31no—
456C2×C3×Dic3—31no—
457C2×C3×Dic3—31no—
458C2×C3×Dic3—31no—
459C2×C3×Dic3—31no—
460C2×C3×Dic3—31no—
461C2×C3×Dic3—31no—
462C2×C3×Dic3—61no—
463C2×C3×Dic3—61no—
464C2×C3×Dic3—61no—
465C2×C3×Dic3—61no—
466C2×C3×Dic3—62no—
467C2×C3×Dic3—62no—
468C2×C3×Dic3—62no—
469C2×C3×Dic3—62no—
470C2×C3×Dic3—122no—
471C2×C3×Dic3—121no—
472C2×C3×Dic3—121no—
473C2×C3×Dic3—121no—
474C2×C3×Dic3—122no—
475C2×C3×Dic3C22×D311yescharacteristic
476C2×C3×Dic3C22×D311yescharacteristic
477C2×C3×Dic3C22×D311yescharacteristic
478C2×C3×Dic3C22×D311yescharacteristic
479C2×C3×Dic3C22×D311yescharacteristic
480C2×C3×Dic3C22×D311yescharacteristic
481C2×C3×Dic3C22×D311yescharacteristic
482C2×C3×Dic3C22×D311yescharacteristic
483C3×D12—62no—
484C3×D12—121no—
485C3×C4×D3—62no—
486C3×C4×D3—62no—
487C3×C4×D3—121no—
488C3×Dic6—62no—
489C3×Dic6—62no—
490#627—22no—
491#626—22no—
492#626—41no—
493#626—64no—
494#626—62no—
495#626—62no—
496#626—121no—
497#626—121no—
498#626—122no—
499#625—22no—
500#625—64no—
501#625—62no—
502#625—62no—
503D3×Dic3—22no—
504D3×Dic3—22no—
505D3×Dic3—41no—
506D3×Dic3—64no—
507D3×Dic3—62no—
508D3×Dic3—62no—
509#546—271noSylow
510C2×C33—22no—
511C2×C33C22×D411yescharacteristic
512C2×C33C2×#4111yescharacteristic
513C2×C33H(5,𝔽2)11yescharacteristic
514C3⋊(C3⋊D3)—41no—
515C3×C3⋊D3—22no—
516C3×C3⋊D3—41no—
517C32×D3—22no—
518C32×D3—41no—
519C24×C3—91no—
520C23×D3—31no—
521C23×D3—31no—
522C23×D3—61no—
523C23×D3—91no—
524C23×D3—91no—
525C23×D3—91no—
526C23×D3—181no—
527C3×#41—184no—
528C2×C3×Q8—91no—
529C2×C3×D4—31no—
530C2×C3×D4—31no—
531C2×C3×D4—31no—
532C2×C3×D4—31no—
533C2×C3×D4—61no—
534C2×C3×D4—61no—
535C2×C3×D4—91no—
536C2×C3×D4—91no—
537C2×C3×D4—91no—
538C22×C3×C4—91no—
539C22×C3×C4—91no—
540C22×C3×C4—91no—
541C22×C3×C4—91no—
542C22×C3×C4—91no—
543C2×#67—31no—
544C2×#67—31no—
545C2×#67—31no—
546C2×#67—31no—
547C2×#67—91no—
548C2×#67—91no—
549C2×#67—91no—
550C2×#67—91no—
551C2×#67—91no—
552C2×#67—91no—
553C2×#67—91no—
554C2×#67—91no—
555C2×#67—91no—
556C2×#67—181no—
557C2×#67—181no—
558C2×#67—181no—
559C2×#67—181no—
560C2×#67—181no—
561C2×#67—184no—
562C2×#67—361no—
563C2×#67D3211yescharacteristic
564C2×#67D3211yescharacteristic, complemented
565C22×Dic3—31no—
566C22×Dic3—31no—
567C22×Dic3—31no—
568C22×Dic3—31no—
569C22×Dic3—31no—
570C22×Dic3—31no—
571C22×Dic3—31no—
572C22×Dic3—61no—
573C22×Dic3—61no—
574C22×Dic3—91no—
575#237—64no—
576#237—64no—
577D3×D4—184no—
578D3×D4—184no—
579D3×D4—188no—
580C2×D12—31no—
581C2×D12—31no—
582C2×D12—91no—
583C2×D12—91no—
584C2×D12—91no—
585C2×D12—181no—
586C2×C4×D3—31no—
587C2×C4×D3—31no—
588C2×C4×D3—31no—
589C2×C4×D3—91no—
590C2×C4×D3—91no—
591C2×C4×D3—181no—
592C2×Dic6—31no—
593C2×Dic6—31no—
594C3×C4⋊C4—91no—
595C3×C22⋊C4—31no—
596C3×C22⋊C4—31no—
597C3×C22⋊C4—61no—
598C3×C22⋊C4—91no—
599C3×C22⋊C4—91no—
600C3×C22⋊C4—91no—
601C3×C42—91no—
602#217—31no—
603#217—91no—
604#217—91no—
605#217—91no—
606#217—91no—
607#217—91no—
608#217—91no—
609#217—181no—
610#217D3211yescharacteristic, complemented
611(C2×D3)⋊C4—31no—
612(C2×D3)⋊C4—31no—
613(C2×D3)⋊C4—31no—
614(C2×D3)⋊C4—31no—
615(C2×D3)⋊C4—31no—
616(C2×D3)⋊C4—91no—
617(C2×D3)⋊C4—91no—
618(C2×D3)⋊C4—91no—
619(C2×D3)⋊C4—91no—
620(C2×D3)⋊C4—91no—
621(C2×D3)⋊C4—91no—
622(C2×D3)⋊C4—91no—
623(C2×D3)⋊C4—91no—
624(C2×D3)⋊C4—91no—
625(C2×D3)⋊C4—91no—
626(C2×D3)⋊C4—91no—
627(C2×D3)⋊C4—91no—
628(C2×D3)⋊C4—91no—
629(C2×D3)⋊C4—91no—
630(C2×D3)⋊C4—91no—
631(C2×D3)⋊C4—91no—
632(C2×D3)⋊C4—91no—
633(C2×D3)⋊C4—91no—
634(C2×D3)⋊C4—181no—
635(C2×D3)⋊C4—181no—
636(C2×D3)⋊C4—181no—
637C4⋊Dic3—31no—
638C4⋊Dic3—91no—
639C4⋊Dic3—91no—
640C4⋊Dic3—91no—
641C4⋊Dic3—91no—
642C4⋊Dic3—91no—
643C4⋊Dic3—181no—
644C4⋊Dic3—181no—
645Dic3⋊C4—31no—
646Dic3⋊C4—91no—
647Dic3⋊C4—91no—
648Dic3⋊C4—91no—
649Dic3⋊C4—91no—
650Dic3⋊C4—181no—
651C4×Dic3—31no—
652C4×Dic3—31no—
653C22×C32—21no—
654C22×C32—21no—
655C22×C32—21no—
656C22×C32—21no—
657C22×C32—21no—
658C22×C32—21no—
659C22×C32—21no—
660C22×C32—21no—
661C22×C32—21no—
662C22×C32—22no—
663C22×C32—22no—
664C22×C32—22no—
665C22×C32—32no—
666C22×C32—41no—
667C22×C32—42no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—41no—
671C22×C32—41no—
672C22×C32—41no—
673C22×C32—41no—
674C22×C32—61no—
675C22×C32—61no—
676C22×C32—61no—
677C22×C32—61no—
678C22×C32—61no—
679C22×C32—81no—
680C22×C32—81no—
681C22×C32C2×D1212yes—
682C22×C32D3×D412yes—
683C22×C32C2×#6712yes—
684C22×C32C23×D311yescharacteristic
685C22×C32C23×D311yescharacteristic
686C22×C32C23×D311yescharacteristic
687C2×C3⋊D3—21no—
688C2×C3⋊D3—21no—
689C2×C3⋊D3—21no—
690C2×C3⋊D3—21no—
691C2×C3⋊D3—21no—
692C2×C3⋊D3—44no—
693C2×C3⋊D3—61no—
694C2×C3⋊D3—62no—
695C2×C3⋊D3—61no—
696C2×C3⋊D3—61no—
697C2×C3⋊D3—61no—
698C2×C3⋊D3—61no—
699C2×C3⋊D3—61no—
700C2×C3⋊D3—61no—
701C2×C3⋊D3—61no—
702C2×C3⋊D3—61no—
703C2×C3⋊D3—121no—
704C2×C3⋊D3—121no—
705C2×C3⋊D3—122no—
706C2×C3⋊D3—121no—
707C2×C3⋊D3—121no—
708C2×C3⋊D3—121no—
709C2×C3⋊D3—121no—
710C2×C3⋊D3—121no—
711C2×C3⋊D3—121no—
712C2×C3⋊D3—124no—
713C2×C3⋊D3—241no—
714C2×C3⋊D3—241no—
715C2×C3⋊D3#23712yescomplemented
716C2×C3×D3—21no—
717C2×C3×D3—21no—
718C2×C3×D3—21no—
719C2×C3×D3—21no—
720C2×C3×D3—21no—
721C2×C3×D3—21no—
722C2×C3×D3—21no—
723C2×C3×D3—21no—
724C2×C3×D3—21no—
725C2×C3×D3—21no—
726C2×C3×D3—22no—
727C2×C3×D3—32no—
728C2×C3×D3—32no—
729C2×C3×D3—41no—
730C2×C3×D3—41no—
731C2×C3×D3—41no—
732C2×C3×D3—41no—
733C2×C3×D3—41no—
734C2×C3×D3—62no—
735C2×C3×D3—62no—
736C2×C3×D3—62no—
737C2×C3×D3—61no—
738C2×C3×D3—61no—
739C2×C3×D3—61no—
740C2×C3×D3—61no—
741C2×C3×D3—62no—
742C2×C3×D3—61no—
743C2×C3×D3—61no—
744C2×C3×D3—61no—
745C2×C3×D3—61no—
746C2×C3×D3—61no—
747C2×C3×D3—61no—
748C2×C3×D3—121no—
749C2×C3×D3—121no—
750C2×C3×D3—124no—
751C2×C3×D3—124no—
752C2×C3×D3—128no—
753C2×C3×D3C2×D1212yes—
754C2×C3×D3C2×#6712yes—
755D32—124no—
756D32—124no—
757D32—128no—
758C32×C4—32no—
759C32×C4—61no—
760C32×C4—61no—
761C32×C4—61no—
762C3⋊Dic3—21no—
763C3⋊Dic3—21no—
764C3⋊Dic3—21no—
765C3⋊Dic3—21no—
766C3⋊Dic3—61no—
767C3⋊Dic3—62no—
768C3⋊Dic3—61no—
769C3⋊Dic3—61no—
770C3⋊Dic3—121no—
771C3⋊Dic3—121no—
772C3⋊Dic3—122no—
773C3×Dic3—21no—
774C3×Dic3—21no—
775C3×Dic3—21no—
776C3×Dic3—21no—
777C3×Dic3—21no—
778C3×Dic3—21no—
779C3×Dic3—22no—
780C3×Dic3—41no—
781C3×Dic3—41no—
782C3×Dic3—41no—
783C3×Dic3—62no—
784C3×Dic3—61no—
785C3×Dic3—61no—
786C3×Dic3—61no—
787C3×Dic3—61no—
788C3×Dic3—61no—
789C3×Dic3—61no—
790C3×Dic3—61no—
791C3×Dic3—61no—
792C3×Dic3—121no—
793C3×Dic3—121no—
794C3×Dic3—121no—
795C3×Dic3C2×D1212yes—
796C3×Dic3C2×#6712yes—
797C2×#41—91no—
798C22×D4—271no—
799#124—271no—
800#123—271no—
801#123—271no—
802C22⋊Q8—271no—
803#121—271no—
804#121—271no—
805#121—271no—
806#120—91no—
807#120—271no—
808C4×D4—91no—
809C4×D4—271no—
810C2×C22⋊C4—271no—
811C2×C22⋊C4—271no—
812C33#54611yescharacteristic, complemented, Sylow
813C23×C3—21no—
814C23×C3—21no—
815C23×C3—21no—
816C23×C3—31no—
817C23×C3—31no—
818C23×C3—31no—
819C23×C3—31no—
820C23×C3—41no—
821C23×C3—61no—
822C23×C3—61no—
823C23×C3—91no—
824C23×C3—91no—
825C23×C3—182no—
826C23×C3—182no—
827C23×C3—361no—
828C23×C3C2×D3211yescharacteristic
829C23×C3C2×D3211yescharacteristic
830C23×C3C2×D3211yescharacteristic
831C22×D3—31no—
832C22×D3—31no—
833C22×D3—31no—
834C22×D3—31no—
835C22×D3—61no—
836C22×D3—61no—
837C22×D3—62no—
838C22×D3—62no—
839C22×D3—64no—
840C22×D3—62no—
841C22×D3—62no—
842C22×D3—91no—
843C22×D3—91no—
844C22×D3—91no—
845C22×D3—122no—
846C22×D3—121no—
847C22×D3—121no—
848C22×D3—122no—
849C22×D3—181no—
850C22×D3—181no—
851C22×D3—181no—
852C22×D3—182no—
853C22×D3—182no—
854C22×D3—182no—
855C22×D3—182no—
856C22×D3—182no—
857C22×D3—184no—
858C22×D3—182no—
859C22×D3—361no—
860C22×D3—362no—
861C22×D3—361no—
862C22×D3—361no—
863C22×D3—361no—
864C22×D3—362no—
865C22×D3C2×D3211yescharacteristic
866C22×D3C2×D3211yescharacteristic
867C3×Q8—182no—
868C3×D4—34no—
869C3×D4—34no—
870C3×D4—64no—
871C3×D4—62no—
872C3×D4—62no—
873C3×D4—122no—
874C3×D4—182no—
875C3×D4—182no—
876C3×D4—361no—
877C2×C3×C4—31no—
878C2×C3×C4—31no—
879C2×C3×C4—31no—
880C2×C3×C4—31no—
881C2×C3×C4—31no—
882C2×C3×C4—31no—
883C2×C3×C4—31no—
884C2×C3×C4—31no—
885C2×C3×C4—61no—
886C2×C3×C4—61no—
887C2×C3×C4—61no—
888C2×C3×C4—61no—
889C2×C3×C4—91no—
890C2×C3×C4—91no—
891C2×C3×C4—91no—
892C2×C3×C4—91no—
893C2×C3×C4—182no—
894C2×C3×C4—182no—
895C2×C3×C4—182no—
896C2×C3×C4—361no—
897C2×C3×C4—361no—
898#67—22no—
899#67—62no—
900#67—62no—
901#67—62no—
902#67—121no—
903#67—182no—
904#67—182no—
905#67—184no—
906#67—184no—
907#67—182no—
908#67—182no—
909#67—182no—
910#67—182no—
911#67—182no—
912#67—362no—
913#67—362no—
914#67—364no—
915#67—361no—
916#67—361no—
917#67—362no—
918#67#62614yescomplemented
919C2×Dic3—31no—
920C2×Dic3—31no—
921C2×Dic3—31no—
922C2×Dic3—31no—
923C2×Dic3—31no—
924C2×Dic3—31no—
925C2×Dic3—31no—
926C2×Dic3—31no—
927C2×Dic3—61no—
928C2×Dic3—61no—
929C2×Dic3—61no—
930C2×Dic3—61no—
931C2×Dic3—62no—
932C2×Dic3—62no—
933C2×Dic3—62no—
934C2×Dic3—62no—
935C2×Dic3—91no—
936C2×Dic3—91no—
937C2×Dic3—91no—
938C2×Dic3—122no—
939C2×Dic3—121no—
940C2×Dic3—121no—
941C2×Dic3—121no—
942C2×Dic3—122no—
943C2×Dic3—181no—
944C2×Dic3—181no—
945C2×Dic3—181no—
946C2×Dic3—182no—
947C2×Dic3—361no—
948C2×Dic3C2×D3211yescharacteristic
949C2×Dic3C2×D3211yescharacteristic
950C2×Dic3C2×D3211yescharacteristic
951C2×Dic3C2×D3211yescharacteristic
952D12—62no—
953D12—121no—
954D12—182no—
955D12—182no—
956D12—184no—
957D12—361no—
958C4×D3—62no—
959C4×D3—62no—
960C4×D3—121no—
961C4×D3—182no—
962C4×D3—182no—
963C4×D3—184no—
964Dic6—62no—
965Dic6—62no—
966C2×C32—22no—
967C2×C32—22no—
968C2×C32—22no—
969C2×C32—21no—
970C2×C32—21no—
971C2×C32—21no—
972C2×C32—21no—
973C2×C32—21no—
974C2×C32—21no—
975C2×C32—21no—
976C2×C32—21no—
977C2×C32—21no—
978C2×C32—41no—
979C2×C32—41no—
980C2×C32—41no—
981C2×C32—42no—
982C2×C32—42no—
983C2×C32—42no—
984C2×C32—62no—
985C2×C32—82no—
986C2×C32—121no—
987C2×C32C22×D1211yescharacteristic
988C2×C32C2×D3×D411yescharacteristic
989C2×C32C2×#23711yescharacteristic
990C2×C32#100411yescharacteristic
991C2×C32#100411yescharacteristic
992C2×C32D3×#4111yescharacteristic
993C2×C32D3×#4111yescharacteristic
994C2×C32#100911yescharacteristic
995C2×C32C22×#6711yescharacteristic
996C3⋊D3—22no—
997C3⋊D3—41no—
998C3⋊D3—121no—
999C3⋊D3—122no—
1000C3⋊D3—121no—
1001C3⋊D3—121no—
1002C3⋊D3—241no—
1003C3⋊D3—241no—
1004C3⋊D3—242no—
1005C3×D3—22no—
1006C3×D3—22no—
1007C3×D3—42no—
1008C3×D3—41no—
1009C3×D3—41no—
1010C3×D3—64no—
1011C3×D3—62no—
1012C3×D3—62no—
1013C3×D3—81no—
1014C3×D3—122no—
1015C3×D3—121no—
1016C3×D3—121no—
1017C24—91no—
1018C24—271no—
1019#41—184no—
1020C2×Q8—91no—
1021C2×D4—31no—
1022C2×D4—31no—
1023C2×D4—91no—
1024C2×D4—91no—
1025C2×D4—91no—
1026C2×D4—271no—
1027C2×D4—271no—
1028C2×D4—271no—
1029C2×D4—271no—
1030C2×D4—544no—
1031C22×C4—91no—
1032C22×C4—91no—
1033C22×C4—91no—
1034C22×C4—91no—
1035C22×C4—91no—
1036C22×C4—271no—
1037C4⋊C4—91no—
1038C4⋊C4—271no—
1039C4⋊C4—271no—
1040C4⋊C4—271no—
1041C22⋊C4—31no—
1042C22⋊C4—91no—
1043C22⋊C4—91no—
1044C22⋊C4—91no—
1045C22⋊C4—271no—
1046C22⋊C4—271no—
1047C22⋊C4—271no—
1048C22⋊C4—271no—
1049C22⋊C4—271no—
1050C22⋊C4—271no—
1051C22⋊C4—271no—
1052C22⋊C4—271no—
1053C42—91no—
1054C22×C3—21no—
1055C22×C3—21no—
1056C22×C3—21no—
1057C22×C3—21no—
1058C22×C3—21no—
1059C22×C3—21no—
1060C22×C3—21no—
1061C22×C3—21no—
1062C22×C3—21no—
1063C22×C3—22no—
1064C22×C3—22no—
1065C22×C3—22no—
1066C22×C3—32no—
1067C22×C3—32no—
1068C22×C3—41no—
1069C22×C3—41no—
1070C22×C3—41no—
1071C22×C3—41no—
1072C22×C3—41no—
1073C22×C3—41no—
1074C22×C3—41no—
1075C22×C3—42no—
1076C22×C3—62no—
1077C22×C3—61no—
1078C22×C3—61no—
1079C22×C3—61no—
1080C22×C3—61no—
1081C22×C3—61no—
1082C22×C3—61no—
1083C22×C3—61no—
1084C22×C3—61no—
1085C22×C3—61no—
1086C22×C3—61no—
1087C22×C3—81no—
1088C22×C3—81no—
1089C22×C3—92no—
1090C22×C3—121no—
1091C22×C3—121no—
1092C22×C3—121no—
1093C22×C3—121no—
1094C22×C3—121no—
1095C22×C3—181no—
1096C22×C3—181no—
1097C22×C3—181no—
1098C22×C3—181no—
1099C22×C3—181no—
1100C22×C3—364no—
1101C22×C3D3×D1212yes—
1102C22×C3C2×#62612yes—
1103C22×C3D3×#6712yes—
1104C22×C3C22×D3211yescharacteristic
1105C22×C3C22×D3211yescharacteristic
1106C22×C3C22×D3211yescharacteristic
1107C2×D3—21no—
1108C2×D3—21no—
1109C2×D3—21no—
1110C2×D3—21no—
1111C2×D3—21no—
1112C2×D3—32no—
1113C2×D3—32no—
1114C2×D3—62no—
1115C2×D3—62no—
1116C2×D3—62no—
1117C2×D3—61no—
1118C2×D3—61no—
1119C2×D3—61no—
1120C2×D3—61no—
1121C2×D3—62no—
1122C2×D3—61no—
1123C2×D3—61no—
1124C2×D3—61no—
1125C2×D3—61no—
1126C2×D3—61no—
1127C2×D3—61no—
1128C2×D3—121no—
1129C2×D3—121no—
1130C2×D3—124no—
1131C2×D3—124no—
1132C2×D3—128no—
1133C2×D3—182no—
1134C2×D3—181no—
1135C2×D3—181no—
1136C2×D3—181no—
1137C2×D3—181no—
1138C2×D3—181no—
1139C2×D3—181no—
1140C2×D3—181no—
1141C2×D3—181no—
1142C2×D3—181no—
1143C2×D3—361no—
1144C2×D3—361no—
1145C2×D3—361no—
1146C2×D3—361no—
1147C2×D3—361no—
1148C2×D3—361no—
1149C2×D3—361no—
1150C2×D3—361no—
1151C2×D3—362no—
1152C2×D3—364no—
1153C2×D3—364no—
1154C2×D3—364no—
1155C2×D3—368no—
1156C2×D3—721no—
1157C2×D3—721no—
1158C2×D3C2×#62612yes—
1159C3×C4—32no—
1160C3×C4—32no—
1161C3×C4—62no—
1162C3×C4—61no—
1163C3×C4—61no—
1164C3×C4—61no—
1165C3×C4—61no—
1166C3×C4—61no—
1167C3×C4—61no—
1168C3×C4—121no—
1169C3×C4—121no—
1170C3×C4—121no—
1171C3×C4—181no—
1172C3×C4—181no—
1173C3×C4—181no—
1174C3×C4—181no—
1175Dic3—21no—
1176Dic3—21no—
1177Dic3—21no—
1178Dic3—62no—
1179Dic3—61no—
1180Dic3—61no—
1181Dic3—61no—
1182Dic3—61no—
1183Dic3—61no—
1184Dic3—61no—
1185Dic3—61no—
1186Dic3—61no—
1187Dic3—121no—
1188Dic3—121no—
1189Dic3—121no—
1190Dic3—182no—
1191Dic3—181no—
1192Dic3—181no—
1193Dic3—181no—
1194Dic3—361no—
1195Dic3—361no—
1196Dic3—362no—
1197Dic3C2×#62612yes—
1198C32—21no—
1199C32—21no—
1200C32—21no—
1201C32—41no—
1202C32#555411yescharacteristic, complemented
1203C32#559111yescharacteristic, complemented
1204C32#582911yescharacteristic, complemented
1205C23—31no—
1206C23—31no—
1207C23—91no—
1208C23—91no—
1209C23—182no—
1210C23—182no—
1211C23—271no—
1212C23—361no—
1213C23—542no—
1214C23—542no—
1215C23—1081no—
1216C23D3311yescharacteristic
1217Q8—182no—
1218D4—34no—
1219D4—62no—
1220D4—182no—
1221D4—182no—
1222D4—361no—
1223D4—542no—
1224D4—542no—
1225D4—542no—
1226D4—1081no—
1227C2×C4—31no—
1228C2×C4—31no—
1229C2×C4—31no—
1230C2×C4—31no—
1231C2×C4—91no—
1232C2×C4—91no—
1233C2×C4—91no—
1234C2×C4—91no—
1235C2×C4—182no—
1236C2×C4—182no—
1237C2×C4—182no—
1238C2×C4—271no—
1239C2×C4—361no—
1240C2×C4—361no—
1241C2×C4—542no—
1242C2×C3—22no—
1243C2×C3—22no—
1244C2×C3—22no—
1245C2×C3—21no—
1246C2×C3—21no—
1247C2×C3—21no—
1248C2×C3—21no—
1249C2×C3—21no—
1250C2×C3—21no—
1251C2×C3—21no—
1252C2×C3—21no—
1253C2×C3—21no—
1254C2×C3—42no—
1255C2×C3—42no—
1256C2×C3—42no—
1257C2×C3—41no—
1258C2×C3—41no—
1259C2×C3—41no—
1260C2×C3—62no—
1261C2×C3—62no—
1262C2×C3—82no—
1263C2×C3—122no—
1264C2×C3—121no—
1265C2×C3—121no—
1266C2×C3—182no—
1267C2×C3—241no—
1268C2×C3—361no—
1269C2×C3C2×D3×D1211yescharacteristic
1270C2×C3D3×#23711yescharacteristic
1271C2×C3D3×#23711yescharacteristic
1272C2×C3#6431211yescharacteristic
1273C2×C3#6431311yescharacteristic
1274C2×C3#6431411yescharacteristic
1275C2×C3#6431411yescharacteristic
1276C2×C3C22×#62611yescharacteristic
1277C2×C3C2×D3×#6711yescharacteristic
1278D3—22no—
1279D3—41no—
1280D3—64no—
1281D3—62no—
1282D3—62no—
1283D3—122no—
1284D3—121no—
1285D3—121no—
1286D3—362no—
1287D3—361no—
1288D3—361no—
1289D3—361no—
1290D3—721no—
1291D3—721no—
1292D3—722no—
1293C22—21no—
1294C22—21no—
1295C22—32no—
1296C22—61no—
1297C22—61no—
1298C22—61no—
1299C22—61no—
1300C22—61no—
1301C22—92no—
1302C22—181no—
1303C22—181no—
1304C22—181no—
1305C22—181no—
1306C22—181no—
1307C22—364no—
1308C22—541no—
1309C22—541no—
1310C22—541no—
1311C22—1084no—
1312C22D3×#62612yes—
1313C22C2×D3311yescharacteristic
1314C4—32no—
1315C4—61no—
1316C4—61no—
1317C4—61no—
1318C4—181no—
1319C4—181no—
1320C4—181no—
1321C4—181no—
1322C4—541no—
1323C3—21no—
1324C3—21no—
1325C3—21no—
1326C3—41no—
1327C3#1059429211yescharacteristic, complemented
1328C3#1059525411yescharacteristic, complemented
1329C3#1059530411yescharacteristic, complemented
1330C2—22no—
1331C2—62no—
1332C2—121no—
1333C2—182no—
1334C2—361no—
1335C2—1081no—
1336C2#1172440811yescharacteristic
1337C2#1172441611yescharacteristic
1338C2C2×D3×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3⋊D3×#67C2semidirect
2. C2×C3×#3805C2semidirect
3. C2×#88814C2semidirect
4. #11723635C2semidirect
5. #11723608C2semidirect
6. C3×#63981C2semidirect
7. C3×#67⋊Dic3C2semidirect
8. #11723003C2semidirect
9. #11722988C2semidirect
10. #11722974C2semidirect
11. #11722959C2semidirect
12. #11722956C2semidirect
13. #11722949C2semidirect
14. Dic3×#626C2semidirect
15. D3×#3722C2semidirect
22. C22×C3×C3⋊Dic3C22semidirect
23. C22×C3×C3⋊Dic3C22semidirect
25. C2×C32×#67C22semidirect
28. C2×#6291C22semidirect
31. C2×C3×#627C22semidirect
33. C2×C3×#626C22semidirect
34. C2×C3×#625C22semidirect
36. C2×C3×D3×Dic3C22semidirect
37. C2×C3×D3×Dic3C22semidirect
38. C2×C3×D3×Dic3C22semidirect
39. C32×#217C22semidirect
42. #88814C22semidirect
43. #88814C22semidirect
44. #88807C22semidirect
45. Dic3⋊(C3⋊Dic3)C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
47. #88804C22semidirect
48. #88804C22semidirect
49. #88804C22semidirect
50. (C2×D3)⋊(C3⋊Dic3)C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
53. C3×#3722C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
62. C2×#3805D3semidirect
71. #63981D3semidirect
77. #67⋊Dic3D3semidirect
125. C32×#67D4semidirect
163. C22×C3⋊Dic3C2×D3semidirect
164. C22×C3⋊Dic3C2×D3semidirect
176. C2×C3×#67C2×D3semidirect
177. C2×C3×#67C2×D3semidirect
199. C2×#627C2×D3semidirect
207. C2×#626C2×D3semidirect
211. C2×#625C2×D3semidirect
216. C2×D3×Dic3C2×D3semidirect
217. C2×D3×Dic3C2×D3semidirect
218. C2×D3×Dic3C2×D3semidirect
229. C3×#217C2×D3semidirect
230. C3×#217C2×D3semidirect
249. Dic3⋊Dic3C2×D3semidirect
264. #3722C2×D3semidirect
276. (C2×D3)⋊Dic3C2×D3semidirect
277. Dic32C2×D3semidirect
291. C2×C3×C3⋊D3#41semidirect
448. C3×#67D12semidirect
449. C3×#67#67semidirect
564. C2×#67D32semidirect
610. #217D32semidirect
715. C2×C3⋊D3#237semidirect
812. C33#546semidirect
918. #67#626semidirect
1202. C32#5554semidirect
1203. C32#5591semidirect
1204. C32#5829semidirect
1327. C3#10594292semidirect
1328. C3#10595254semidirect
1329. C3#10595304semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3⋊D3×#672
C2×C3×#38052
C2×#888142
#117236352
#117236082
C3×#639812
C3×#67⋊Dic32
#117230032
#117229882
#117229742
#117229592
#117229562
#117229492
Dic3×#6262
D3×#37222
#105953043
#105952543
#105942923